(a) Write the differential equation given by the Evans price adjustment model for the price p as a function of time. (Use k for the constant of proportionality.)   dp/dt=k   (c) Find the particular solution in which Eggbert dolls are initially priced at $10 and the price rises to $12 after one month. p(t)=

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The Extrasoft Toy Co. has just released its latest creation, a plush platypus named "Eggbert." The demand function for Eggbert dolls is 

D(p) = 49,000 − 500p dolls per month

 when the price is p dollars. The supply function is 

S(p) = 30,000 + 500p dolls per month

 when the price is p dollars. This makes the equilibrium price $19. The Evans price adjustment model assumes that if the price is set at a value other than the equilibrium price, it will change over time in such a way that its rate of change is proportional to the shortage 

D(p) − S(p).
 
(a) Write the differential equation given by the Evans price adjustment model for the price p as a function of time. (Use k for the constant of proportionality.)
 
dp/dt=k
 
(c) Find the particular solution in which Eggbert dolls are initially priced at $10 and the price rises to $12 after one month.
p(t)=
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